Molecular Shape Hybridization

Of the various geometric parameters associated with molecular shape, the one most nearly constant from molecule to molecule and most nearly independent of substituent effects is bond length. Bond lengths to carbon depend strongly on the hybridization of the carbon involved but are little influenced by other factors. Table 1.2 lists the interatomic distances for some of the most common bonds in organic molecules. The near constancy of bond lengths from molecule to molecule reflects the fact that the properties of individual bonds are, to a good approximation, independent of the remainder of the molecule. 

FIGURE 3.16 Three common hybridization schemes shown as outlines of the amplitude of the wavefunction and in terms of the orientations of the hybrid orbitals, (a) An s-orbital and a p-orbital hybridize into two sp hybrid orbitals that >oint in opposite direc tions, forming a linear molecular shape, (b) An s-orbital and two p-orbitals can blend together to give three ip hybrid orbitals that point to the corners of an equilateral triangle, (c) An s-orbital and three p-orbitals can blend together to give four sp hybrid orbitals that point to the corners of a tetrahedron. 

Self-Test 3.8A Describe (a) the electron arrangement, (b) the molecular shape, and (c) the hybridization of the central chlorine atom in chlorine trifluoride. 

Hiroshima, 721 histidine, 443, 774 hole, 195 homeostasis, 386 HOMO, 126, 580 homogeneous alloy, 202 homogeneous catalyst, 565 homogeneous equilibria, 362 homogeneous mixture, F53 homolytic dissociation, 80 homonuclear diatomic molecule, 103 Hooke s law, 92 hormone, 670 horsepower, A4, 791 hour, A4 HPLC, 354 HRF products, 723 HTSC, 192 Humphreys series, 51 Hund, F 35 Hund s rule, 35, 37 Hurricane Rita, 144 hyaluronic acid, 344 hybrid orbital, 109 hybridization bond angle, 131 molecular shape, 111 hydrangea color, 463 hydrate, F32 hydrate isomer, 676 hydration, 178 hydrazine, 627... 

Remember that the molecular shape ignores the lone pair. The hydronium ion has a trigonal pyramidal shape described by the three s p hybrid orbitals that form bonds to hydrogen atoms. 

To relate the hybrid angles of Table 4.3 to idealized molecular shapes, let us now consider a general MI./, species with k monovalent ligands L.13 In general, k equivalent sd hybrids of sd/, 1 composition (i.e., p = k — 1) are needed to form the sigma skeleton... 

By combining the skeletal hybrid composition (4.44) with the bond angles of Table 4.3, we can recognize the idealized molecular shape(s) corresponding to each ML coordination. 

Figure 4.3 Idealized ML4 molecular shapes for equivalent sd3 hybridization (cf. (4.47a)-(4.47c) in the text), with optimal L—M—L bond angles owe = 70.53° or tfobtuse = 109.47° for all ligands.

Figure 4.4 Idealized ML5 molecular shapes having (limited) similarity with optimal L—M—L bond angles cWe = 65.91° and a0btuse = 114.09° of equivalent sd4 hybridization.

Figure 4-5 Idealized MLg molecular shapes for equivalent sd5 hybridization (cf. (A 49a)—(4 49d)in 1116 text) wittl °Ptimal L—M—L bond angles a acute = 63.43°...

Figure 4.6 Relationships of idealized sd -1 -hybridized ML molecular shapes to simple polyhedra. Each panel shows the hybrid-orbital axes in dumbbell dz2 -like form embedded within the polyhedron, together with the associated allowed (no-hms-vertex) dispositions of ligands on the polyhedral vertices (with the unmarked metal atom occupying the polyhedral centroid in each case) (a) sd1 square, (b) sd2 octahedron, (c) sd3 cube, and (d) sd5 icosahedron.

C3V o shape (Fig. 4.5(a)), ReH5 (Fig. 4.7(b)) resembles the idealized ML5 Cs shape (Fig. 4.4(a)), OsH4 (Fig. 4.7(c)) is the idealized ML4 Td shape (Fig. 4.3(a)), and so forth. Thus, the rather unusual hydride geometries immediately suggest the role of sdM hybridization and covalency, leading to molecular shapes quite unlike those expected from simple ionic or packing ( VSEPR-like 15) forces.16... 

Although orbital hybridizations and molecular shapes for hypovalent metal hydrides of the early transition metals and the normal-valent later transition metals are similar, the M—H bonds of the early metals are distinctly more polar. For example, metal-atom natural charges for YH3 (+1.70), HfH4 (+1.75), and TaHs (+1.23) are all significantly more positive than those (ranging from +0.352 to —0.178) for the homoleptic hydrides from groups 6-10. Indeed, the empirical chemistry of early transition-metal hydrides commonly reveals greater hydricity than does that of the later transition-metal hydrides. 

However, the important new feature of metal alkylidenes (4.51) is metal-carbon pi-bonding. As discussed in Section 2.8, pi bonds between transition metals and main-group elements are of d -p type, much stronger than corresponding p —pn bonds between heavier main-group elements. Compared with simple metal hydrides and alkyls, metal-carbon pi-bonding in metal alkylidenes affects the selection of metal d orbitals available for hybridization and skeletal bond formation, somewhat altering molecular shapes. 

In summary, the Lewis-like model seems to predict the composition, qualitative molecular shape, and general forms of hybrids and bond functions accurately for a wide variety of main-group derivatives of transition metals. The sd-hybridization and duodectet-rule concepts for d-block elements therefore appear to offer an extended zeroth-order Lewis-like model of covalent bonding that spans main-group and transition-metal chemistry in a satisfactorily unified manner. 

It is clear that the combination of different architectures and the precise localization of functionalities within a single macromolecule provide unique opportunities for the control of molecular shape as well as molecular, optical, and electronic properties. A significant hurdle that still remains today is the relatively demanding multistep process used to prepare dendrons and hybrids. This, in turn, translates into limited availability but, as high added-value applications emerge, it is clear that current, as well as yet-to-be-developed, syntheses will be used to prepare specialty materials that benefit from the unique properties derived from the combination of dendritic and linear architectures. 

The AO s of carbon can hybridize in ways other than sp as shown in Fig. 2-7. Repulsion between pairs of electrons causes these HO s to have the maximum bond angles and geometries summarized in Table 2-2. The sp and sp HO s induce geometries about the C s as shown in Fig. 2-8. Only a bonds, not v bonds, determine molecular shapes. 

Although the discussions of the preceding molecules have been couched in valence bond terms (Lewis structures, hybridization, etc.), recall that the criterion for molecular shape (rule 2 above) was that the cr bonds of the central atom should be allowed to gel as far from each other as possible 2 at 180°. 3 at 120°, 4 at 109.5°, etc. This is (he heart of the VSEPR method of predicting molecular structures, and is, indeed, independent of valence bond hybridization schemes, although it is most readily applied in a VB context. 

It is important to realize that methane is not tetrahedral because carbon has sp3, hybrid orbitals. Hybridization is only a model—a theoretical way of describing the bonds that are needed for a given molecular structure. Hybridization is an interpretation of molecular shape shape is not a consequence of hybridization. 

Describe the molecular shape and the hybridization of the central atom in sulfur tetrafluoride, SF4. 

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